Event Detail

Event Type: 
Analysis Seminar
Date/Time: 
Monday, October 15, 2012 - 05:00
Location: 
Kidder 356

Speaker Info

Local Speaker: 
Abstract: 

We discuss the standard plate equations (Kirchoff, Euler-Bernoulli, von
Karman) which arise in modeling the oscillations of thin membranes. The
dynamics of these models are highly dependent upon the nature of the
nonlinearity (nonlocal, cubic-type) and on the physical parameter which
corresponds to the thickness of the plate (and is regularizing for the
dynamics). The models under consideration are important in the mathematical
study of wing and panel flutter, when the plate is coupled to a flow
equation.

In the first talk, we discuss the model in full generality and introduce the
abstract setup needed for the semigroup approach. We then restrict to a
specific case (linear plate equation with nonlinear interior damping).
Well-posedness of this model will be demonstrated. In the sequel, we discuss
the well-posedness of the fully nonlinear model in the presence of the von
Karman nonlinearity (non-compact). Time permitting, the discussion will
include a dynamical systems approach to long-time behavior of solutions,
including stability estimates from multiplier methods. As the nonlinear
model has non-trivial stationary solutions, we will show the existence of a
compact, finite-dimensional global attractor in the state space.